you could put a drop down list of the ship states on the cart page, you would need to add a new form, to the page, and make sure the form is not inside the cart display form when the ship state is selected, they would need to submit it, then you would need to store the selection in a session variable.
It is very similar;ar to adding a coupon code system, except instead of creating Discount based on the session value, you create a tax rule based on the session value.
We have a tutorial on the eCart support page for creating the coupon code system that will give the basic background on how to do this, it is really the same concept:
ecart/
look in the archived documentation section, it was written for eCrt 4 but the steps ae the same for eCart 5.
